Finite Group Databasebeta

← #34056940

Subgroups — #34056940

Order 19072.

392 conjugacy classes of subgroups.

The subgroup lattice has 370 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#23750319C211yesmaximal, characteristic, complemented
2#23750286C211yesmaximal, characteristic, complemented
3#23749981C211yesmaximal, characteristic, complemented
4#23749954C211yesmaximal, characteristic, complemented
5#23749949C211yesmaximal, characteristic, complemented
6#23749930C211yesmaximal, characteristic, complemented
7#23749878C211yesmaximal, characteristic, complemented
8#23749874C211yesmaximal, characteristic, complemented
9#23749843C211yesmaximal, characteristic, complemented
10#23749773C211yesmaximal, characteristic, complemented
11#23749764C211yesmaximal, characteristic, complemented
12#23749710C211yesmaximal, characteristic, complemented
13#23749701C211yesmaximal, characteristic, complemented
14#23749625C211yesmaximal, characteristic, complemented
15#419×C149C211yesmaximal, characteristic, complemented
16C2×#14558737C2211yescharacteristic
17C2×#14558723C2211yescharacteristic
18C2×#14558723C2211yescharacteristic
19C2×D1192C2211yescharacteristic
20C2×#14558719C2211yescharacteristic
21#18011905—21no—
22#18011902C2211yescharacteristic
23#18011900—21no—
24#18011900C2211yescharacteristic
25#18011893—21no—
26#18011887—21no—
27#18011887C2211yescharacteristic
28#18011886C2211yescharacteristic
29#18011885—21no—
30#18011885C2211yescharacteristic
31#18011885C2211yescharacteristic
32#18011884—21no—
33Q8×Dic149C2211yescharacteristic
34C4×D596—21no—
35#18011873C2211yescharacteristic
36C4×C22⋊D149—21no—
37C4×C22⋊D149C2211yescharacteristic
38C4⋊C4×D149C2211yescharacteristic
39#18011844C2211yescharacteristic
40#18011843C2211yescharacteristic
41#18011842C2211yescharacteristic
42#18011840C2211yescharacteristic
43#18011835C2211yescharacteristic
44#18011835C2211yescharacteristic
45#18011833C2211yescharacteristic
46#18011833C2211yescharacteristic
47#18011831C2211yescharacteristic
48#18011831C2211yescharacteristic
49C22⋊#11924746C2211yescharacteristic
50#18011823C2211yescharacteristic
51C8×Dic149C2211yescharacteristic
52C22×Q8×C149C2211yescharacteristic
53C2×M16×C149C2211yescharacteristic
54#117×C149C2211yescharacteristic
55#103×C149C2211yescharacteristic
56#103×C149C2211yescharacteristic
57#103×C149C2211yescharacteristic
58#103×C149C2211yescharacteristic
59#14558737—22no—
60#14558737—41no—
61C2×D596—21no—
62C2×D596—21no—
63C2×D596C2311yescharacteristic
64C2×D596C2311yescharacteristic
65C2×C22⋊D149—21no—
66C2×C22⋊D149—21no—
67C2×C22⋊D149D411yescharacteristic
68C2×C4×D149—21no—
69C2×C4×D149—21no—
70C2×C4×D149—21no—
71C2×C4×D149C2311yescharacteristic
72#14558723—22no—
73#14558723—41no—
74D1192—41no—
75#14558719—41no—
76C2×#11924746C2311yescharacteristic
77C2×#11924746C2311yescharacteristic
78C4⋊Dic149—21no—
79C4⋊Dic149—21no—
80C4⋊Dic149C2311yescharacteristic
81C4⋊Dic149C2311yescharacteristic
82#14558715—21no—
83#14558715—21no—
84#14558715—21no—
85#14558715D411yescharacteristic
86C22⋊Dic149D411yescharacteristic
87#14558713—21no—
88#14558713—21no—
89#14558713—21no—
90#14558713—21no—
91#14558713—21no—
92#14558713—21no—
93#14558713—21no—
94#14558713D411yescharacteristic
95C4×Dic149—21no—
96C4×Dic149C2311yescharacteristic
97C2×Q8×C149—21no—
98C2×Q8×C149—22no—
99C2×Q8×C149—41no—
100C2×Q8×C149C2311yescharacteristic
101C2×Q8×C149C2311yescharacteristic
102C22×C4×C149—21no—
103C22×C4×C149C2311yescharacteristic
104M16×C149—41no—
105C2×C8×C149C2311yescharacteristic
106C2×C8×C149C2311yescharacteristic
107C4⋊C4×C149C2311yescharacteristic
108C4⋊C4×C149C2311yescharacteristic
109C22⋊C4×C149—21no—
110C42×C149—21no—
111C22×D149—21no—
112C22×D149—21no—
113C22×D149C2×D411yescharacteristic
114D596—21no—
115D596—21no—
116D596—21no—
117D596—21no—
118D596—42no—
119D596—42no—
120C22⋊D149—41no—
121C22⋊D149—42no—
122C22⋊D149—81no—
123C2×Dic149—21no—
124C2×Dic149—21no—
125C2×Dic149C2×D411yescharacteristic
126C2×Dic149C2×D411yescharacteristic
127C2×Dic149C2×D411yescharacteristic
128C4×D149—21no—
129C4×D149—21no—
130C4×D149—42no—
131C4×D149—81no—
132C4×D149—81no—
133#11924746—21no—
134#11924746—21no—
135C23×C149C2×D411yescharacteristic
136Q8×C149—21no—
137Q8×C149—21no—
138Q8×C149—21no—
139Q8×C149—42no—
140Q8×C149#4112yes—
141C2×C4×C149—21no—
142C2×C4×C149—21no—
143C2×C4×C149—21no—
144C2×C4×C149—21no—
145C2×C4×C149—21no—
146C2×C4×C149—21no—
147C2×C4×C149—42no—
148C2×C4×C149C2×D411yescharacteristic
149C2×C4×C149C2411yescharacteristic
150C8×C149—21no—
151C8×C149—21no—
152C22×C149—21no—
153C22×C149—21no—
154C22×C149—21no—
155C22×C149C22×D411yescharacteristic
156C2×D149—21no—
157C2×D149—21no—
158C2×D149—21no—
159C2×D149—41no—
160C2×D149—41no—
161C2×D149—41no—
162C2×D149—41no—
163C2×D149—41no—
164C2×D149—41no—
165C4×C149—21no—
166C4×C149—22no—
167C4×C149—41no—
168C4×C149—41no—
169C4×C149—41no—
170C4×C149C2×#4111yescharacteristic
171C4×C149H(5,𝔽2)11yescharacteristic
172Dic149—21no—
173Dic149—21no—
174Dic149—21no—
175Dic149—41no—
176Dic149—41no—
177C2×C149—41no—
178C2×C149#54611yescharacteristic
179C2×C149#57511yescharacteristic
180C2×C149#57711yescharacteristic
181D149—41no—
182D149—81no—
183D149—81no—
184C149#332611yescharacteristic, complemented, Sylow
185#3326—1491nomaximal, Sylow
186#553—1491no—
187#548—1491no—
188#488—1491no—
189#483—1491no—
190#482—1491no—
191#479—1491no—
192#469—1491no—
193#468—1491no—
194#463—1491no—
195#449—1491no—
196#448—1491no—
197C4×SD16—1491no—
198#436—1491no—
199#419D14911yescharacteristic, complemented
200#417—1491no—
201C2×#41—1491no—
202C22×Q8C2×D14911yescharacteristic
203C2×SD16—1491no—
204C2×SD16—1491no—
205C2×D8—1491no—
206C2×M16—1491no—
207C2×M16C2×D14911yescharacteristic
208#126—2981no—
209#125—1491no—
210#124—2981no—
211#124—1491no—
212#123—2981no—
213C22⋊Q8—2981no—
214C22⋊Q8—1491no—
215#121—2981no—
216#121—2981no—
217#121—1491no—
218#121—1491no—
219#121—1491no—
220C4×Q8—1491no—
221C4×D4—2981no—
222C4×D4—2981no—
223C4×D4—1491no—
224C4×D4—1491no—
225#117C2×D14911yescharacteristic
226C2×C4⋊C4—1491no—
227#107—1491no—
228#106—1491no—
229#106—1491no—
230C4⋊C8—1491no—
231#103—1491no—
232#103—1491no—
233#103C2×D14911yescharacteristic
234#103C2×D14911yescharacteristic
235#103C2×D14911yescharacteristic
236#103C2×D14911yescharacteristic
237#102—1491no—
238#102—1491no—
239#102—1491no—
240#102—1491no—
241C22⋊C8—1491no—
242C22⋊C8—1491no—
243C4×C8—1491no—
244#41—2982no—
245#41—5961no—
246C2×Q8—21no—
247C2×Q8—22no—
248C2×Q8—41no—
249C2×Q8C22×D14911yescharacteristic
250C2×Q8C22×D14911yescharacteristic
251C2×D4—2981no—
252C2×D4—2981no—
253C2×D4—2981no—
254C2×D4—2981no—
255C2×D4—1491no—
256C2×D4—1491no—
257C2×D4—1491no—
258C22×C4—21no—
259C22×C4—2981no—
260C22×C4—2981no—
261C22×C4—2981no—
262C22×C4—1491no—
263C22×C4C22×D14911yescharacteristic
264SD16—2982no—
265SD16—5961no—
266D8—5961no—
267M16—41no—
268M16—5961no—
269C2×C8—1491no—
270C2×C8—1491no—
271C2×C8C22×D14911yescharacteristic
272C2×C8C22×D14911yescharacteristic
273C4⋊C4—2981no—
274C4⋊C4—2981no—
275C4⋊C4—2981no—
276C4⋊C4—2981no—
277C4⋊C4—2981no—
278C4⋊C4—1491no—
279C4⋊C4—1491no—
280C4⋊C4—1491no—
281C4⋊C4C22×D14911yescharacteristic
282C4⋊C4C22×D14911yescharacteristic
283C22⋊C4—21no—
284C22⋊C4—2981no—
285C22⋊C4—2981no—
286C22⋊C4—2981no—
287C22⋊C4—2981no—
288C22⋊C4—2981no—
289C22⋊C4—2981no—
290C22⋊C4—2981no—
291C22⋊C4—1491no—
292C22⋊C4—1491no—
293C42—21no—
294C42—2981no—
295C42—1491no—
296C23—2981no—
297C23—2981no—
298C23—1491no—
299C23D4×D14911yescharacteristic
300Q8—21no—
301Q8—21no—
302Q8—21no—
303Q8—42no—
304Q8#1455873612yes—
305D4—2981no—
306D4—2981no—
307D4—2981no—
308D4—2981no—
309D4—5962no—
310D4—5962no—
311D4—5961no—
312D4—5962no—
313D4—11921no—
314C2×C4—21no—
315C2×C4—21no—
316C2×C4—21no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—42no—
321C2×C4—2981no—
322C2×C4—2981no—
323C2×C4—2981no—
324C2×C4—2981no—
325C2×C4—5962no—
326C2×C4—1491no—
327C2×C4—1491no—
328C2×C4—1491no—
329C2×C4—11921no—
330C2×C4—11921no—
331C2×C4D4×D14911yescharacteristic
332C2×C4C23×D14911yescharacteristic
333C8—21no—
334C8—21no—
335C8—2981no—
336C8—2981no—
337C22—21no—
338C22—21no—
339C22—21no—
340C22—2981no—
341C22—2981no—
342C22—2981no—
343C22—5961no—
344C22—5961no—
345C22—5961no—
346C22—5961no—
347C22—5961no—
348C22—5961no—
349C22C2×D4×D14911yescharacteristic
350C4—21no—
351C4—22no—
352C4—41no—
353C4—41no—
354C4—41no—
355C4—2981no—
356C4—2981no—
357C4—2981no—
358C4—5961no—
359C4—5961no—
360C4C2×#1455873611yescharacteristic
361C4#1801195611yescharacteristic
362C2—41no—
363C2—5961no—
364C2—11921no—
365C2—11921no—
366C2#2375026511yescharacteristic
367C2#2375042411yescharacteristic
368C2#2375043411yescharacteristic
subgroupG/H
centerC22C2×D4×D149
commutator, cosocleC2×C4×C149C24
FrattiniC2×C4C23×D149
Fitting#419×C149C2
socleC22×C149C22×D4
hypercenter#419D149
hypocenterC149#3326
LCSG ▷ C2×C4×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C22 ◁ C22×C4 ◁ #419

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. #23750319C2semidirect
2. #23750286C2semidirect
3. #23749981C2semidirect
4. #23749954C2semidirect
5. #23749949C2semidirect
6. #23749930C2semidirect
7. #23749878C2semidirect
8. #23749874C2semidirect
9. #23749843C2semidirect
10. #23749773C2semidirect
11. #23749764C2semidirect
12. #23749710C2semidirect
13. #23749701C2semidirect
14. #23749625C2semidirect
15. #419×C149C2semidirect
184. C149#3326semidirect
199. #419D149semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#237503192
#237502862
#237499812
#237499542
#237499492
#237499302
#237498782
#237498742
#237498432
#237497732
#237497642
#237497102
#237497012
#237496252
#419×C1492
#3326149